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Taper Diameters, Length & Half-Angle Calculator

Calculate diametral taper and the side-to-axis half-angle from two diameters and an axial length.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A major diameter of 30 mm, minor diameter of 10 mm and taper length of 10 mm give a diametral taper of 2 mm/mm and a half-angle of 45°. The full included cone angle is twice that half-angle.

Diametral taper = (major diameter − minor diameter) ÷ axial length; half-angle = atan(diametral taper / 2)

Worked example

Enter these known values and leave the other values blank.

Major diameter Dₗ
30 mm
Minor diameter Dₛ
10 mm
Axial taper length L
10 mm
Side-to-axis half-angle θ
45 deg
Diametral change per length
0.07874015748031496063 in / mm

Assumptions and limitations

  • Use positive diameters and axial length, with the major diameter larger than the minor diameter. This model accepts positive half-angles below its approximately 89° upper bound.
  • The taper ratio has independently selected numerator and denominator length units. Use matching units for a dimensionless ratio, or explicitly read a mixed-unit result such as inches per millimeter.
  • This is straight-sided cone or frustum geometry. It does not select a standardized machine-tool taper or a machining tolerance.

Common questions

Is the displayed angle the full included angle?

No. It is the half-angle between one side and the axis. Double it to obtain the full included cone angle.

Is taper per inch based on radius change?

This model uses diameter change divided by length. The factor of two in the angle formula converts that diameter change to the radius change on one side.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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